Volume 26, 2020
|Number of page(s)||34|
|Published online||17 July 2020|
Analysis of the controllability from the exterior of strong damping nonlocal wave equations*
University of Puerto Rico, Rio Piedras Campus, Department of Mathematics, College of Natural Sciences, 17 University AVE. STE 1701,
PR 00925-2537, USA.
2 Universidad de Santiago de Chile, Facultad de Ciencia, Departamento de Matemática y Ciencia de la Computación, Casilla 307-Correo 2, Santiago, Chile.
** Corresponding author: firstname.lastname@example.org
Accepted: 24 April 2019
We make a complete analysis of the controllability properties from the exterior of the (possible) strong damping wave equation associated with the fractional Laplace operator subject to the non-homogeneous Dirichlet type exterior condition. In the first part, we show that if 0 < s < 1, Ω ⊂ ℝN (N ≥ 1) is a bounded Lipschitz domain and the parameter δ > 0, then there is no control function g such that the following system
is exact or null controllable at time T > 0. In the second part, we prove that for every δ ≥ 0 and 0 < s < 1, the system is indeed approximately controllable for any T > 0 and g ∈ D(O × (0,T)), where O ⊂ ℝN \ Ω is any non-empty open set.
Mathematics Subject Classification: 35R11 / 35S05 / 35S11 / 35L20 / 93B05
Key words: Fractional Laplace operator / wave equation / strong damping / exterior control / exact and null controllabilities / approximate controllability
© EDP Sciences, SMAI 2020
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